Amortized quadrature for posterior expectations in inverse problems
Uncertainty in the solution of an inverse problem and in the tasks performed on it is quantified by posterior expectations, each an average of an integrand over $M$ posterior samples. While designed quadratures improve on the $O(M^{-1/2})$ error of Monte-Carlo estimation, they solve an optimization problem, often against the posterior density, for every new observation, which can be computationally costly. To address this limitation, we introduce the quadrature field, a set-equivariant network that maps an observation and its $M$ posterior samples to an $M$-node signed-weight quadrature in one forward pass. Trained once on a family of posteriors to minimize the worst-case integration erro...
| Authors | Ali Siahkoohi |
|---|---|
| Primary category | stat.CO |
| Published | 14 June 2026 |
| Last updated at source | 25 September 2026 |
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